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A firm uses capital and labor to produce output according to the production function q =4 rad(KL) , for which MP L= 2 rad(K/L) and MP K= 2 rad(L/K) .
a. If the wage w=$1/labor-hr. and the rental rate of capital r=$4/machine-hr., what is the least expensive way to produce 16 units of output?
b. What is the minimum cost of producing 16 units?
c. Show that for any level of output, q, the minimum cost of producing q is $q.
d. Explain how a 10% wage tax would affect the way in which the firm chooses to produce any given amount of output.
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Suppose there are two types of movie: Arty (A), and Popcorn (P). These films may be either Decent (D) or Terrible (T). 35% of all movies are Arty. 20% of all movies are both Arty and Decent. If a film is a Popcorn, there is a 75% chance that it is Te..
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Suppose the mayor is suggesting an increase in gas taxes that would affect the commute costs and thus bid rent curves for residents Pr=5.5-0.75x. Calculate the new size of the city.
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